论文标题
双重覆盖的同源组中的Betti数字和扭转
Betti numbers and torsions in homology groups of double coverings
论文作者
论文摘要
Papadima和Suciu证明了具有有限的野外系数和扭曲的共同体学组的同类综合体组的等级之间的不平等，并猜想它们实际上在与该布置的Milnor纤维相关的某些情况下相等。最近，发现了具有以下两个特性的布置（Icosidododecahedrespement）：（i）Papadima-Suciu的不平等现象的严格版本，以及（ii）Milnor Fiber的第一个积分同源性具有非宽松的$ 2 $ -Torsion。在本文中，我们研究了这两种属性之间的关系，以进行双层覆盖空间。我们证明（i）和（ii）实际上是等效的。
Papadima and Suciu proved an inequality between the ranks of the cohomology groups of the Aomoto complex with finite field coefficients and the twisted cohomology groups, and conjectured that they are actually equal for certain cases associated with the Milnor fiber of the arrangement. Recently, an arrangement (the icosidodecahedral arrangement) with the following two peculiar properties was found: (i) the strict version of Papadima-Suciu's inequality holds, and (ii) the first integral homology of the Milnor fiber has a non-trivial $2$-torsion. In this paper, we investigate the relationship between these two properties for double covering spaces. We prove that (i) and (ii) are actually equivalent.
